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Algorithms for Coloring Reconfiguration Under Recolorability Digraphs

Authors Soichiro Fujii , Yuni Iwamasa , Kei Kimura , Akira Suzuki

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Author Details

Soichiro Fujii
  • Research Institute for Mathematical Sciences, Kyoto University, Japan
  • School of Mathematical and Physical Sciences, Macquarie University, Sydney, Australia
Yuni Iwamasa
  • Graduate School of Informatics, Kyoto University, Japan
Kei Kimura
  • Faculty of Information Science and Electrical Engineering, Kyushu University, Fukuoka, Japan
Akira Suzuki
  • Graduate School of Information Sciences, Tohoku University, Sendai, Japan

Funding

  • Fujii, Soichiro: Partially supported by JST, ERATO Grant Number JPMJER1603 (HASUO Metamathematics for Systems Design Project) and JSPS Overseas Research Fellowships.
  • Iwamasa, Yuni: Partially supported by JSPS KAKENHI Grant Numbers JP20K23323, JP20H05795, 22K17854, Japan.
  • Kimura, Kei: Partially supported by JSPS KAKENHI Grant Numbers JP19K22841, JP21K17700, Japan.
  • Suzuki, Akira: Partially supported by JSPS KAKENHI Grant Numbers JP18H04091, JP20K11666, JP20H05794, Japan.

Cite AsGet BibTex

Soichiro Fujii, Yuni Iwamasa, Kei Kimura, and Akira Suzuki. Algorithms for Coloring Reconfiguration Under Recolorability Digraphs. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 4:1-4:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.ISAAC.2022.4

Abstract

In the k-Recoloring problem, we are given two (vertex-)colorings of a graph using k colors, and asked to transform one into the other by recoloring only one vertex at a time, while at all times maintaining a proper k-coloring. This problem is known to be solvable in polynomial time if k ≤ 3, and is PSPACE-complete if k ≥ 4. In this paper, we consider a (directed) recolorability constraint on the k colors, which forbids some pairs of colors to be recolored directly. The recolorability constraint is given in terms of a digraph R, whose vertices correspond to the colors and whose arcs represent the pairs of colors that can be recolored directly. We provide algorithms for the problem based on the structure of recolorability constraints R, showing that the problem is solvable in linear time when R is a directed cycle or is in a class of multitrees.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
Keywords
  • combinatorial reconfiguration
  • graph coloring
  • recolorability
  • recoloring

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References

  1. Marthe Bonamy, Matthew Johnson, Ioannis Lignos, Viresh Patel, and Daniël Paulusma. Reconfiguration graphs for vertex colourings of chordal and chordal bipartite graphs. Journal of Combinatorial Optimization, 27(1):132-143, 2014. URL: https://doi.org/10.1007/s10878-012-9490-y.
  2. John Adrian Bondy and Uppaluri Siva Ramachandra Murty. Graph Theory, volume 244 of Graduate Texts in Mathematics. Springer, 2008. Google Scholar
  3. Paul Bonsma and Luis Cereceda. Finding paths between graph colourings: Pspace-completeness and superpolynomial distances. Theoretical Computer Science, 410(50):5215-5226, 2009. URL: https://doi.org/10.1016/j.tcs.2009.08.023.
  4. Luis Cereceda, Jan van den Heuvel, and Matthew Johnson. Finding paths between 3-colorings. Journal of Graph Theory, 67(1):69-82, 2011. URL: https://doi.org/10.1002/jgt.20514.
  5. Erik D. Demaine, Isaac Grosof, Jayson Lynch, and Mikhail Rudoy. Computational complexity of motion planning of a robot through simple gadgets. In Proceedings of the 9th International Conference on Fun with Algorithms (FUN 2018), volume 100 of LIPIcs, pages 18:1-18:21. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. URL: https://doi.org/10.4230/LIPIcs.FUN.2018.18.
  6. Erik D. Demaine, Dylan H. Hendrickson, and Jayson Lynch. Toward a general complexity theory of motion planning: Characterizing which gadgets make games hard. In Proceedings of the 11th Innovations in Theoretical Computer Science Conference (ITCS 2020), volume 151 of LIPIcs, pages 62:1-62:42. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. URL: https://doi.org/10.4230/LIPIcs.ITCS.2020.62.
  7. Dorit Dor and Uri Zwick. Sokoban and other motion planning problems. Computational Geometry, 13(1):215-228, 1999. URL: https://doi.org/10.1016/S0925-7721(99)00017-6.
  8. Michael R. Garey and David S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, San Francisco, CA, 1979. Google Scholar
  9. Tatsuhiko Hatanaka, Takehiro Ito, and Xiao Zhou. The list coloring reconfiguration problem for bounded pathwidth graphs. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 98-A(6):1168-1178, 2015. URL: https://doi.org/10.1587/transfun.E98.A.1168.
  10. Jan van den Heuvel. The complexity of change. Surveys in Combinatorics 2013, 409:127-160, 2013. URL: https://doi.org/10.1017/CBO9781139506748.005.
  11. Takehiro Ito, Erik D. Demaine, Nicholas J. A. Harvey, Christos H. Papadimitriou, Martha Sideri, Ryuhei Uehara, and Yushi Uno. On the complexity of reconfiguration problems. In Proceedings of the 19th Annual International Symposium on Algorithms and Computation (ISAAC 2008), volume 5369 of Lecture Notes in Computer Science, pages 28-39, 2008. URL: https://doi.org/10.1007/978-3-540-92182-0_6.
  12. Takehiro Ito, Erik D. Demaine, Nicholas J. A. Harvey, Christos H. Papadimitriou, Martha Sideri, Ryuhei Uehara, and Yushi Uno. On the complexity of reconfiguration problems. Theoretical Computer Science, 412:1054-1065, 2011. URL: https://doi.org/10.1016/j.tcs.2010.12.005.
  13. Takehiro Ito, Yuni Iwamasa, Yasuaki Kobayashi, Yu Nakahata, Yota Otachi, Masahiro Takahashi, and Kunihiro Wasa. Independent set reconfiguration on directed graphs. In Proceedings of the 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022), to appear. Google Scholar
  14. Matthew Johnson, Dieter Kratsch, Stefan Kratsch, Viresh Patel, and Daniël Paulusma. Finding shortest paths between graph colourings. Algorithmica, 75(2):295-321, 2016. URL: https://doi.org/10.1007/s00453-015-0009-7.
  15. Bernhard Korte and Jens Vygen. Combinatorial Optimization. Springer, sixth edition, 2018. URL: https://doi.org/10.1007/978-3-662-56039-6.
  16. Kazuo Murota. Discrete Convex Analysis. Monographs on Discrete Mathematics and Applications. SIAM, 2003. URL: https://doi.org/10.1137/1.9780898718508.
  17. Naomi Nishimura. Introduction to reconfiguration. Algorithms, 11(4):52, 2018. URL: https://doi.org/10.3390/a11040052.
  18. Hiroki Osawa. Coloring Reconfiguration Problems and Their Generalizations. PhD thesis, Tohoku University, 2020. Google Scholar
  19. Hiroki Osawa, Akira Suzuki, Takehiro Ito, and Xiao Zhou. Complexity of Coloring Reconfiguration under Recolorability Constraints. In Proceedings of the 28th International Symposium on Algorithms and Computation (ISAAC 2017), volume 92 of Leibniz International Proceedings in Informatics (LIPIcs), pages 62:1-62:12. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2017. URL: https://doi.org/10.4230/LIPIcs.ISAAC.2017.62.
  20. Hiroki Osawa, Akira Suzuki, Takehiro Ito, and Xiao Zhou. Algorithms for coloring reconfiguration under recolorability constraints. In Proceedings of the 29th International Symposium on Algorithms and Computation (ISAAC 2018). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2018. URL: https://doi.org/10.4230/LIPIcs.ISAAC.2018.37.
  21. Alexander Schrijver. Theory of Linear and Integer Programming. John Wiley & Sons, 1998. Google Scholar
  22. Roni Stern, Nathan R. Sturtevant, Ariel Felner, Sven Koenig, Hang Ma, Thayne T. Walker, Jiaoyang Li, Dor Atzmon, Liron Cohen, T. K. Satish Kumar, Roman Barták, and Eli Boyarski. Multi-agent pathfinding: Definitions, variants, and benchmarks. In Proceedings of the 12th International Symposium on Combinatorial Search (SOCS 2019), pages 151-159. AAAI Press, 2019. Google Scholar
  23. Marcin Wrochna. Reconfiguration in bounded bandwidth and tree-depth. Journal of Computer and System Sciences, 93:1-10, 2018. URL: https://doi.org/10.1016/j.jcss.2017.11.003.
  24. Marcin Wrochna. Homomorphism reconfiguration via homotopy. SIAM Journal on Discrete Mathematics, 34(1):328-350, 2020. URL: https://doi.org/10.1137/17M1122578.
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